Write an equation in point-slope form of the line that passes through (-2, 5) and (1, -1)

Answer 1

Write an equation in point-slope form of the line that passes through (-2, 5) and (1, -1)

(x₁, y₁) = (-2, 5) and (x₂, y₂) = (1, -1)

Slope: m = (y₂ – y₁)/ (x₂ – x₁) = (-1 – 5)/ (1 – (-2)) = -6/3 = -2 ==> m = -2

Equation in point-slope form:

y – y₁ = m(x – x₁) ==> y – 5 = -2(x – (-2)) ==> y – 5 = -2(x + 2)

Or

y – y₂ = m(x – x₂) ==> y - (-1) = -2(x –1) ==> y + 1 = -2(x - 1)

Equation in slope-intercept form: m = -2, (x₁, y₁) = (-2, 5) and (x₂, y₂) = (1, -1)

y = mx + b ==> y = -2x + b ==> 5 = -2(-2) + b ==> 5 = 4 + b ==> b = 5 - 4 ==> b = 1 ==> y = -2x + 1

Or

y = mx + b ==> y = -2x + b ==> -1 = -2(1) + b ==> -1 = -2 + b ==> b = -1 + 2 ==> b = 1 ==> y = -2x + 1

Equation in standard form:

Ax + By = C ==> y = -2x + 1 ==> 2x + y = 1

Check: (x₁, y₁) = (-2, 5)

2x + y = 1 ==> 2(-2) + 5 = 1 ==> -4 + 5 = 1 ==> 1 = 1

Check: (x₂, y₂) = (1, -1)

2x + y = 1 ==> 2(1) + (-1) = 1 ==> 2 - 1 = 1 ==> 1 = 1

Answer 2

m = y2 - y1/x2 - x1 (find the slope)

m = (-1 - 5)/(1-(-2)) = -6/3 = -2 (slope)

Point Slope form:

y - y1 = m(x- x1)

so, y - 5 = -2(x - (-2)) or y - (-1) = -2(x - 1)

Solution: y - 5 = -2(x + 2) or y + 1 = -2(x - 1)

Answer 3

(5+1)/(-2-1) = (y+1)/(x-1)

You can "massage" this form into the form required.